4. For the curve with y = -2x3 + x - 6, find:

Question

(b.) the gradient at the point (-1, -5)

(c.) the equation of the tangent line at the point (-1, -5).

Answer 1

y = -2x^3 + x - 6
dy/dx = -6x + 1

at (-1,-5), dy/dx = -6(-1) + 1 = 7

so y = -7x + b
at (-1,-5)
-5 = -7(-1) + b
b = -12

equation of tangent is y = -7x - 12

Answer 2

y = -2x^3 + x - 6
dy/dx = -6x + 1

at (-1,-5), dy/dx = -6(-1) + 1 = 7

so y = -7x + b
at (-1,-5)
-5 = -7(-1) + b
b = -12

equation of tangent is y = -7x - 12